Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Review - True-False Quiz: 1

Answer

True

Work Step by Step

$$\int_a^b[f(x) + g(x)]dx = \lim\limits_{n \to \infty}\sum_{i=1}^n[f(x_i) + g(x_i)]\Delta x$$ $$= \lim\limits_{n \to \infty}[\sum_{i=1}^nf(x_i)\Delta x + \sum_{i=1}^ng(x_i)\Delta x]$$ $$= \lim\limits_{n \to \infty}[\sum_{i=1}^nf(x_i)\Delta x ]+ \lim\limits_{n \to \infty}[\sum_{i=1}^ng(x_i)\Delta x]$$ $$= \int_a^b f(x)dx + \int_a^b g(x)dx$$
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